Einführung in die Bachelor-Studiengänge Mathematik
Wednesday, 13.10.21, 10:30-11:30, Hörsaal Rundbau, Albertstr. 21a
Einführung in den Master-of-Science-Studiengang Mathematik
Wednesday, 13.10.21, 12:30-13:30, Raum 404, Ernst-Zermelo-Str. 1
Einführung in den Master-of-Education-Studiengang Mathematik
Wednesday, 13.10.21, 13:30-14:30, Raum 404, Ernst-Zermelo-Str. 1
Vorstellung der Schwerpunktgebiete des Mathematischen Instituts
Thursday, 14.10.21, 14:00-15:00, BigBlueButton
Numerische Simulation und Optimierung stationärer Gasflüsse
Tuesday, 19.10.21, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
European transmission gas networks are expected to play a major role for the transition to green energy supply as transition technology and for transporting and storing green gas as generated from green energy sources. They are endangered by a wide range of potential disruptions, for example ageing and corrosion, physical damage through construction works (third party interference) and attacks, cyber-attacks and coordinated attack vectors. Hence the determination of the effects of local damage events on the\nsupply of consumers and network elements is required for a variety of individual events and combinations of events. Against this background, (0-dimensional) simulations are\nused to predict and model gas pressures at nodes and gas volume flows for each pipeline. This can be realized by solving algebraic equations using numerical optimization\nwith the aim of minimizing a given objective function subject to equality and inequality constraints. Representative network examples within the context of the EU project SecureGas are generated from published sample grids, inspection of existing maps and literature on gas transport on the level of European transmission grids. Thus, gas grids with realistic lengths, diameters and pressure boundary conditions, the external and internal inflows, outflows and possibly also storage capabilities are generated. Using such representative networks, network models are created for which the effects of potential\ndisruptions are calculated predictively and systematically. For this purpose, the number of nodes not supplied and the pressure loss in nodes that are no longer supplied sufficiently are determined given defined full, single or multiple disruptions.
Classes in Zakharevich K-groups constructed from Quillen K-theory
Friday, 22.10.21, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
(joint work with M. Groechenig)\n\nThe Grothendieck ring of varieties K0(Var) is defined a lot like K0\nin Quillen K-theory. However, vector bundles get replaced by varieties\nand instead of quotienting out exact sequences, we quotient out Z -> X\n<- U relations, where Z is a closed subvariety and U its open\ncomplement.\nThis ring plays a crucial role in motivic integration, as in the proof\nthat K-equivalent [that's yet another meaning of K...] varieties have\nthe same Hodge numbers.\n\n Even though things look very analogous, K0(Var) is not the K0 group\nof some abelian category (or Waldhausen etc). Usual K-theory\nfoundations do not apply. Zakharevich and Campbell established that\nthere is an analogous theoretical formalism nonetheless, so there are\nalso higher K-groups corresponding to K(Var). However, until recently,\nit was not known whether any such Kn(Var) for n>0 contains any\nnon-zero element beyond torsion classes. Some months ago, we managed to\ngive the first construction of such, indeed showing that for all odd\nn>=3 the group Kn(Var) is infinite-dimensional. To do this, we develop\ntwo new tools. Joint with M. Groechenig and A. Nanavaty, motivic\nrealizations give rise to maps out of K(Var), and (joint just with M.\nGroechenig) there is a kind of exponential map from Quillen K-theory to\nK(Var), allowing us to import Quillen K-theory classes to give rise to\nclasses living on abelian varieties in K(Var).
Finite element methods for 1D few-particle quantum dynamics
Tuesday, 26.10.21, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
The dynamics of one-dimensional few-particle quantum systems are key to understand the phenomenological differences between single- and many-body systems, and ultimately the transition to the thermodynamic limit. While experimentally such systems become increasingly controllable, exact numerical approaches are feasible but challenging.\n\nIn this talk, we start with a short introduction to the theoretical description of closed quantum systems. We then demonstrate a numerical treatment of two or three indistinguishable, interacting bosons in a one-dimensional trapping potential, by diagonalization of the many-body Hamiltonian after discretization in an appropriate finite element basis. Along the way, we analyse the convergence properties of our approach and briefly comment on (questions concerning) the mathematical structure of the problem.
Digitales Lernmaterial zur Netflix Challenge (Sek. II)
Tuesday, 26.10.21, 19:30-20:30, Hörsaal II, Albertstr. 23b
Wie kann Netflix Nutzer/innen passende Filmempfehlungen aussprechen? So lautete die Aufgabe der Netflix Challenge, die der Streamingdienst 2006 ausschrieb. Wir haben zu eben dieser Challenge und dem veröffentlichten Datensatz digitales Lernmaterial entwickelt und in mathematischen Modellierungsprojekten mit Schüler/innen erprobt. Auf digitalen Arbeitsblättern erkunden die Lernenden zuerst den Datensatz und erarbeiten anschließend ein mathematisches Modell eines Empfehlungssystems. Durch das Lernmaterial erhalten sie einen Einblick in wesentliche Strategien der mathematischen Modellierung und des Maschinellen Lernens. Das Material zeigt exemplarisch wie datenlastige Problemstellungen aufbereitet und im Distanzlernen / in Präsenz durchgeführt werden können. Der Vortrag bietet einen Einblick in die Problemstellung, das mathematische Modell und die digitale Umsetzung des online verfügbaren Lernmaterials.
Algebraic independence and special functions
Friday, 29.10.21, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
In this talk we are going to see that the solutions of many linear functional equations do not satisfy algebraic differential equations. As an application, we will see how it yields to the proof of the algebraic independence of some special functions.\n\nThis is a joint work with B. Adamczewski, C. Hardouin and M. Wibmer